code: def test_dynamic_factor():
      steps = 10
      exog = np.random.normal(size=steps)
  
      # DFM: 2 series, AR(2) factor
      mod1 = dynamic_factor.DynamicFactor(
          [[0, 0]], k_factors=1, factor_order=2
      )
      mod2 = sarimax.SARIMAX([0], order=(2, 0, 0))
      actual = mod1.impulse_responses(
          [-0.9, 0.8, 1.0, 1.0, 0.5, 0.2], steps
      )
      desired = mod2.impulse_responses([0.5, 0.2, 1], steps)
      assert_allclose(actual[:, 0], -0.9 * desired)
      assert_allclose(actual[:, 1], 0.8 * desired)
  
      # DFM: 2 series, AR(2) factor, exog
      mod1 = dynamic_factor.DynamicFactor(
          np.zeros((steps, 2)), k_factors=1, factor_order=2, exog=exog
      )
      mod2 = sarimax.SARIMAX([0], order=(2, 0, 0))
      actual = mod1.impulse_responses(
          [-0.9, 0.8, 5, -2, 1.0, 1.0, 0.5, 0.2], steps
      )
      desired = mod2.impulse_responses([0.5, 0.2, 1], steps)
      assert_allclose(actual[:, 0], -0.9 * desired)
      assert_allclose(actual[:, 1], 0.8 * desired)
  
      # DFM, 3 series, VAR(2) factor, exog, error VAR
      # TODO: This is just a smoke test
      mod = dynamic_factor.DynamicFactor(
          np.random.normal(size=(steps, 3)),
          k_factors=2,
          factor_order=2,
          exog=exog,
          error_order=2,
          error_var=True,
          enforce_stationarity=False,
      )
      mod.impulse_responses(mod.start_params, steps)
  
imports: from statsmodels.compat.pandas import MONTH_END
  import warnings
  import numpy
  from numpy.testing import assert_, assert_allclose
  import pandas
  import pytest
  from scipy.stats import ortho_group
  from statsmodels.tools.sm_exceptions import EstimationWarning
  from statsmodels.tsa.statespace import dynamic_factor, mlemodel, sarimax, structural, varmax
  from statsmodels.tsa.vector_ar.tests.test_var import get_macrodata
label_desc: Use image node_id 4 for calling a global function with example usage: test_dynamic_factor() without return types